Divergence estimation for multidimensional densities via k-nearest-neighbor distances

A new universal estimator of divergence is presented for multidimensional continuous densities based on -nearest-neighbor ( -NN) distances. Assuming independent and identically distributed (i.i.d.) samples, the new estimator is proved to be asymptotically unbiased and mean-square consistent. In experiments with high-dimensional data, the -NN approach generally exhibits faster convergence than previous algorithms. It is also shown that the speed of convergence of the -NN method can be further improved by an adaptive choice of .